• When to use a median vs a mean

• Dealing with skewed, non-normal data

• Dealing with outliers

• When to transform the scale

Seven Urban Legends in Environmental Statistics

• Do parametric methods have more power than nonparametric tests?

• Why t-tests on logarithms don't test differences in means

• Why t-tests don't test whether one group has higher values than the second

and more....

How Hypothesis Tests Work

• Structure of hypothesis testing

• Their jargon explained

• Parametric, nonparametric and permutation tests. When to use each.

• 1-sided and 2-sided tests

• Checking data distributions

• Illustration: How tests obtain a p-value

Statistical Intervals

• Confidence, prediction, tolerance intervals

• Intervals with small sample sizes

• Coping with skewed data

• Bootstrap intervals — and why to use them instead of t-intervals

• Exercise: the UCL95 and other intervals

• Are means, medians different?

• Parametric, nonparametric and permutation tests

• Testing paired data

• Have standards been met?

• The quantile test

• Permutation tests — test the mean for non-normal distributions

Comparing Three or More Groups

• One- and two-factor ANOVA

• Nonparametric Kruskal-Wallis test

• Multiple comparison tests: who’s different?

• Permutation one-factor test: never worry about a normal distribution again!

Contingency Tables

• Does the frequency change between groups?

• Application to nondetect and other cateogories

• Bootstrapping contingency tables

Testing differences in Variability/Precision

• Characterizing differences in variability

• Levene’s & Fligner-Killeen tests

• Why NOT to use Bartlett’s test

• Linear and monotonic correlation

• r, rho and tau

• Permutation test for Pearson’s r correlation

• The Theil-Sen line: a linear median

Linear Regression

• Building a good regression model

• Better measures of quality than r-squared

• Hypothesis tests, confidence and prediction intervals

• Consequences of transforming the Y variable

• Bootstrapping tests for significance - an alternative to transformations

Multiple Regression

• How to build a good multiple regression model

• Why plots of Y vs each X don't work, and what to do instead

• Multi-collinearity

• Model selection methods better than r-squared or stepwise

• Bootstrapping tests for significance - an alternative to transformations

• Testing whether there is one or more than one regression line

• Are there differences in intercept and slope?

• Modeling seasonal changes

Trend Analysis

• Selecting a trend test

• Regression vs. Mann-Kendall approaches

• Monotonic vs. step trends

• Dealing with seasonality: the Seasonal-Kendall test for trend

• Detecting consistent regional trends across sites

• R routines for trend testing

Final Exam

• Why not substitute 1/2 the detection limit?

• Simple methods without substitution

• Introduction to survival analysis methods

Logistic Regression

• Regression for categorical responses

• Effect of X variables on the odds

• Modeling nondetects, qualitative methods, and the probability of something bad happening

• Multicollinearity and hypothesis tests

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